not sure about any recent regulations but use to accept the odd aircraft ppr after a good brief, It use to be in lockyears farm strip guide.
Been in there a few times in various aircraft. I also use to be a member when i was flying gliders. Its a really nice friendly club with a few motorgliders based there as well.
They use to accept visiting light aircraft with grass strip experience. The only restrictions were you got a good briefing on the day and donated a landing fee to the coffee fund. and there was a sign in book so customs at brize could keep an eye on who was using the strip.
Not sure as to the current situation, could be a local nimby thing. Might be worth giving them a call for a one off